60 research outputs found

    Tangential and normal Euler numbers, complex points, and singularities of projections for oriented surfaces in four-space

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    For a compact oriented smooth surface immersed in Euclidean four-space (thought of as complex two-space), the sum of the tangential and normal Euler numbers is equal to the algebraic number of points where the tangent plane is a complex line. This follows from the construction of an explicit homology between the zero-chains of complex points and the zero-chains of singular points of projections to lines and hyperplanes representing the tangential and normal Euler classes

    Counting tritangent planes of space curves

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    Reproduktionsmedizin bei Muslimen: säkulare und religiöse Ethiken im Widerstreit?

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    Fragen der Reproduktionsmedizin bei Muslimen werden anhand der Fallbeispiele Indien, Ägypten und Mali vorgestellt. Zusätzlich wird die Frage diskutiert, ob bioethische Debatten sich mit einer Einteilung in säkulare vs. religiöse Lager sinnvoll analysieren lassen

    The Politics of the European Research Area. ACES Working Paper 2002.3, August 2002

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    At their Lisbon summit in March 2000, European Union leaders endorsed an ambitious goal: to make the EU “the most competitive and dynamic knowledge-based economy in the world” by the year 2010 (European Council, 2000). This was visionary rhetoric. But it was also more than that. While the ambition of surpassing the United States may or may not be realistic, European leaders are clearly committed to it in both word and deed. They continue to articulate the goal of being number one. And they have initiated a range of policies designed to bring the goal within reach -- everything from the successful introduction of a single currency to competition policy reform and a range of Internet initiatives. This paper examines a key part of this effort, the “European Research Area” (ERA). Launched in January 2000 and endorsed in Lisbon, the ERA is an ambitious effort to pool European scientific and technological resources more effectively. This paper seeks to explain the emergence of the ERA initiative, its initial successes in the face of considerable resistance, and its implications for both the study of European integration and EU efforts to compete with the United States

    Germany's European Policy: A Constructivist Perspective. CES Germany & Europe Working Papers, No. 08.1, 1998

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    This paper sets out a constructivist analytical framework and applies it to post-reunification German policy towards the European Union. Although the structural constraints facing Germany shifted dramatically with the end of the Cold War and reunification, the direction of its European policy did not. The more powerful Federal Republic continued to press for deeper economic and political integration, eschewing a more independent or assertive foreign policy course. Neorealism, neoliberalism, and liberalism cannot adequately explain this continuity in the face of structural change; a constructivist account centered around state identity can. During and after reunification, German leaders across the political spectrum identified the Federal Republic as part of an emergent supranational community. This European identity, with roots in the postwar decades, drove Germany's unflagging support for deeper integration across the 1989-90 divide

    Shadows of Reality: The Fourth dimension in relativity, Cubism, and modern thought

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    Beyond the third dimension: geometry, computer graphics, and higher dimensions

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